Methods and systems for high confidence utilization of datasets

ABSTRACT

Methods and systems for high-confidence utilization of datasets are disclosed. In one embodiment, the method includes selecting a metric for determining substantially optimal combination of true positives and false positives in a data set, applying an optimization technique, and obtaining, from the results of the optimization technique, a value for at least one optimization parameter, the value for at least one optimization parameter resulting in substantially optimal combination of true positives and false positives. A number of true positives and a number of false positives are a function of the one or more optimization parameters.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation in part of co-pending U.S. patentapplication Ser. No. 13/279,514, which is a continuation of U.S. patentapplication Ser. No. 12/355,195, entitled METHODS AND SYSTEMS FOR HIGHCONFIDENCE UTILIZATION OF DATASETS, filed on Jan. 16, 2009, which is adivisional of U.S. patent application Ser. No. 11/497,926, filed Aug. 2,2006, entitled METHODS AND SYSTEMS FOR HIGH CONFIDENCE UTILIZATION OFDATASETS, which in turn claims priority of U.S. Provisional ApplicationSer. No. 60/705,083, filed Aug. 3, 2005, entitled METHODS FOR HIGHCONFIDENCE UTILIZATION OF HIGH-THROUGHPUT DATASETS, and of U.S.Provisional Application Ser. No. 60/705,589, filed Aug. 4, 2005,entitled METHODS FOR HIGH CONFIDENCE UTILIZATION OF HIGH-THROUGHPUTDATASETS, all of which are incorporated by reference herein in theirentirety and for all purposes.

BACKGROUND

The present teachings relate to methods and systems for high-confidenceutilization of large-scale datasets.

The recent sequencing of large number of genomes including human anddevelopment of arraying and other high-throughput technologies hasresulted in increasing utility of these advances to study organismalscale data (cells, tissues, organisms etc.). With these advances andincreasing output of large-scale and high-throughput data has increasedneed for methods and systems to utilize the data with high confidence(i.e., reduce false discovery) to optimally allocate resources forfurther development of concepts, hypotheses, technologies and products.Many of these technologies have been developed in the last decade andtheir quality is constantly improving, and so are the tools to utilizethe datasets and to further refine the technologies. Here a few conceptsand tools are presented that satisfy some of the needs of the lattergoals.

Many systems used in large-scale measurements of organismal/cellularstate involves multiple independent measurements of each parameter(e.g., genes/transcripts/proteins etc.). Two common forms of this typeof technology that are widely used are (i) GeneChip® (Affymetrix,Calif.), where each transcript of a genome is measured using multipleindependent probes, with each probe having a corresponding mismatchprobe to estimate cross-hybridization—the former called a perfect match(PM) probe and the latter mismatch probe (MM)—(well described in patentsand literature; e.g. U.S. Pat. Nos. 6,551,784, 6,303,301) (ii) typicalmeasures of mixtures of proteins as peptide fragments using severalvariations mass spectrometry (e.g., Washburn et. al., 2001 and manyvariations for direct and comparative applications). A variety ofapplications of this type of multiple independent measurements of eachparameter are currently in use and can be envisaged. Due to welldocumented prior knowledge (in literature and in patents) and evolvingapplications, the use of the technologies and generation of the data arenot described here.

Most biological experiments (due to limitations of biological and otherresources) utilizing such high-throughput data generation systems areconducted with small number of replicates. When possible the resultantdata is analyzed using statistical or mathematical principles (forexample to detect differentials between datasets exploring differentconditions) to increase the confidence of the downstream steps used.But, the small number of replicates significantly reduce the statisticalpower in the analyses, in principle, the utilization of the independentmeasures of each parameter should alleviate significant part of thisproblem (at least in terms of improving power with respect to technicalaspects of all steps of the process—e.g., manufacturing, handling,hybridization etc.). In the utilization of multiple independent measuresthere is a need for an understanding of the system specific propertiesand the behavior of the different parameters used in such analyses withrespect to each other. Conversely, understanding properties of suchdatasets would help design better measurement technologies.

Whether applied to datasets with design principles similar to aboveexample (multiple measures of each parameter under each condition) orotherwise the datasets across different conditions and replicationscomparable should be available. This step in data analysis is usuallytermed normalization (in this document used to represent the step afterpre-processing data for technological design and data-collectionspecific effects, e.g., background correction). A good normalization isprerequisite to all further analysis and interpretations of the data.

The above brief background outlines the need i.e., constantly evolvingtechnology and newer algorithms being proposed and no uniform orconsensus approach been accepted and even lesser methods are acceptedand predictably useful in dealing with multiple independent measures ofeach parameter (without an intermediate processing into a unified modelbased summary) highlights the need for improvements that would satisfythe many emerging needs in efficient and productive utilization of thedeluge of data being generated in life sciences and other fields, andsets the stage for one kind of dataset being part of the invention.

SUMMARY

In one embodiment, the method of the present teachings includesselecting a metric for determining substantially optimal combination oftrue positives and false positives in a data set, applying anoptimization technique, and obtaining, from the results of theoptimization technique, a value for at least one optimization parameter,the value for at least one optimization parameter resulting insubstantially optimal combination of true positives and false positives.A number of true positives and a number of false positives are afunction of the one or more optimization parameters.

The system behavior in terms of true and false positives is typicallyviewed as an appropriate response surface of the key parameters. Inanother embodiment, the method of the present teachings for summarizingparameter value includes grouping measurement result from a data setinto a number of pairs of measurement results, determining, for each onepair of measurement results, whether predetermined measures for the onepair of measurement results satisfy threshold criteria, classifying apair of measurement results from the number of pairs of measurementresults as not changing if the predetermined measures do not satisfy thethreshold criteria; comparing, if the predetermined measures satisfiedthe threshold criteria, one measurement result in each one pair ofmeasurement results to another measurement result in each one pair ofmeasurement results, classifying, after the comparison, each one pair ofmeasurement results according to result of the comparison. selecting acommon set of measurement results from the classified plurality of pairsof measurement result for use with the data set, and providing summarymeasures for a parameter utilizing the common set. Various embodimentsthat present parameter estimation methods, data normalization methodsand methods for testing quality of analyses are disclosed. In addition,embodiments of systems and computer program products are also disclosed.

For a better understanding of the present invention, together with otherand further needs thereof, reference is made to the accompanyingdrawings and detailed description and its scope will be pointed out inthe appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts a flowchart representation of an embodiment of the methodof the present teachings;

FIGS. 2 a, 2 b depict a flowchart representation of another embodimentof the method of the present teachings;

FIGS. 3 a, 3 b depicts a flowchart representation of the embodiment ofthe method of the present teachings shown in FIGS. 2 a, 2 b;

FIG. 4 depicts a flowchart representation of a section of the embodimentshown in FIG. 3 a, 3 b;

FIG. 5 depicts a flowchart representation of yet another embodiment ofthe method of the present teachings;

FIG. 6 and FIG. 7 depict a flowchart representation of a furtherembodiment of the method of the present teachings;

FIG. 8, FIG. 9 and FIG. 10 depict an embodiment of the method of thepresent teachings for expression summary;

FIG. 11 depict another embodiment of the method of the present teachingsto estimate fold change;

FIG. 12 depicts a further embodiment of the method of the presentteachings to estimate confidence measure;

FIG. 13 depicts yet another embodiment of the method of the presentteachings to test quality of data analyses tools used;

FIG. 14 depicts yet a further embodiment of the method of the presentteachings in normalizing data;

FIG. 15 depict an embodiment to develop a computer system to practicethe present teachings;

FIG. 16 depicts a graphical schematic representation of results from anembodiment of the method of the present teachings;

FIG. 17 depicts another graphical schematic representation of resultsfrom an embodiment of the method of the present teachings;

FIGS. 18A, 18B depict effect of parameters on results of interest in oneembodiment of the method of these teachings;

FIG. 19 depicts results of an exemplary embodiment of the method ofthese teachings; and

FIG. 20 shows an exemplary spectrum on which measurements are performed.

DETAILED DESCRIPTION

In one embodiment, the present teachings include a set of methods andalgorithms to aid high-confidence utilization of large-scale datasets,viz., (a) a response surface assisted strategy to study datasetsrepresented by multiple measurements of each parameter (especially usingindependent aspects of the same parameter) and aid in design of suchmeasurement technologies and schemes, (b) methods for determiningdata-specific thresholds, (c) to test the efficacy of a selectionstrategy (statistical and/or mathematical) in the data analysis scheme,and (d) a new normalizing scheme for making datasets comparable.

Additional information on the data types being discussed and terminologyused to describe these teachings is disclosed below.

While attempting to describe the teachings in generic scenario, theAffymetrix GeneChip® technology is used as example often, forconvenience. Some design aspects of this technology would serve tohighlight, but not limited to, the multiple measures type datasetdiscussed here. In the GeneChip® system each transcript is representedby eleven or more 25 nucleotide long probes complementary to the mRNA toprobe the transcriptional status of the system being studied. Acorresponding mismatch probe to represent the cross-hybridization signal(would be considered probe-specific noise) is included in the chip. Highfeature densities have been achieved and known and predicted transcriptshave been arrayed onto one to few chips for human and other organisms.While the mismatch probes is included to represent thecross-hybridization or probe-specific noise signal and is used in thatsense in examples described here, other variations (and applications)that do not include these MM probes (e.g., as suggested in dCHIP:www.dchip.org and Irizarry et. al. 2003) are equally well utilized bythe approaches described as part of this set of teachings, andadvantages if any would directly translate in the outcome.

Due to the physico-chemical properties of the probes and hybridizationeach probe though representing a single transcript (i.e., transcriptexpressed at a particular quantal level) has different hybridizationintensity levels. This leads to difficulties in direct utilization ofthe signal levels. One common approach that has been extensivelyresearched on and being continually developed is to use model basedapproaches to summarize the data represented by multiple probes into asingle summary measure for each transcript (see U.S. Pat. No. 6,571,005,which is incorporated by reference herein). This approach has theadvantage of user friendly representation of the data and in ease ofutilization in advanced statistical and mathematical applications forthe utilization of the data in the context of advancement of knowledgeof the system/process being studied (using pattern recognition,classifiers for diagnostics, identification and study of pathways andnew processes, lead candidates for product development etc.).

Other applications are within the scope of these teachings. For example,many fluorescent and other spectral and wave based sensors can bedesigned to similar form of multiple measures of each parameter to getsubstantially optimal differentiation of true and false positives. Forthese purposes one knows or determines the form/characteristic of aspectrum being measured (e.g., emission spectrum of green fluorescentprotein or a fluorophore—FIG. 20). Now one can use a combination measure(e.g., a number of measurements at relevant parts of the spectrum) andthe number of measures can be optimized using parameters and a costfunmction as described in this disclosure. In FIG. 20, this measurementstrategy is depicted by vertical lines for wavelengths to be measured onan example emission spectrum to be measured. One can significantlyeliminate stray signals (as happens during by using measurement of thatsignal at a single wavelength—as is currently the standard) by suchcombination measures based on knowledge of the spectral properties ofthe target being measured (e.g., emission spectrum of green fluorescentprotein, as mentioned above). This becomes especially important assensitivity and throughput of measurements are increased and there is aneed to use the output data accurately. Some examples of instrumentationused currently are nucleic acid sequencing, high spatial density offluorescent signals on a miniaturized chip etc. The applicability can beextended to analyze complete wave signal measured, to reduce thecomputational cost (be it in terms of speed or resources need forcomputation). The effect of a variety of factors (impurities, dust andfibers etc.) are well documented. An example is the following extractand reference. “Fluorescence is a very sensitive technique. This is theone criterion that makes it a viable replacement to manyradioisotope-labeling procedures. However, it is extremely susceptibleto interference by contamination of trace levels of organic chemicals.Potential sources of contamination are ubiquitous since any aromaticorganic compound can be a possible source of fluorescence signal. Forexample, the researcher is a possible source of this type ofcontamination since oils secreted by the skin are fluorescent. Goodlaboratory procedure is essential in preventing solvents and chemicalsfrom becoming contaminated with high background fluorescence that couldhinder low-level measurements. Solvents should be of the highest levelpurity obtainable commercially. In addition, care must be taken toeliminate all forms of solid interference (suspended particulates suchas dust and fibers). These will float in and out of the sampling area ofthe cuvette via convection currents, and cause false signals due tolight scattering while they remain in the instrument's beam.”[http://fmrc.pulmec.washington.edu/DOCUMENTS/FMRC299.pdf]

Yet another application in which the methods of these teachings can beapplied is the use offset measures of sensor based measurements tosubstantially alter the measured characteristic. This can be at thelevel of placement of sensors or design aberrations that accomplish thisneed. The use of the independently measured inputs of the same featureprovides ways to achieve substantially optimum combinations of true andfalse positive outcomes using approaches disclosed herein below. Thecost function in this case will reflect the design and manufacture oranalysis needs. An example is Spatially Offset Raman Spectroscopy (wherean optimal number of N for a given requirement of substantially optimaldetection of true and false positive measures, as disclosed hereinbelow, would be useful). In these cases both design of measurement andanalysis of measured feature can be accomplished, the number of measurescan be optimized to get significantly optimal combination of true andfalse positives as a function, using the methods of these teachings.

Some conventions used in this description are described herein below.

Throughout this text and in the accompanying figures the term parameteris used in two context specific manner: (i) to describe eachexperimental feature within a dataset (transcript, protein etc.), and(ii) thresholds and other calculated numbers used in the process ofutilizing the invention(s) in statistical and mathematical sense. Inaddition the difference between a calculated value and a set ofcalculated/estimated or designated threshold is differentiated by asuperscripted single quote (for example distance designated d would bed′ when used as threshold).

The use of term independent measures simply imply measures of oneparameter (transcript etc.) using entirely different measurementcriteria (e.g., different regions of a transcript as probe, differentregions of a protein—peptide fragments, more than one antibody tomeasure a protein etc.,—while the different region might have physicaloverlap it could have different signal properties under the samecondition. This explicitly differentiates from the concept ofstatistical independence. Indeed some of the properties being studied,proposed and advanced here arise due to this difference. The embodimentsdescribed herein are not limited to this type of statisticalindependence.

An embodiment of the method of these teachings, a Response surface aidedstrategy (also referred to as ReSurfX) for the study of datasets isdescribed herein below, where each parameter is measured using multipleindependent measurements

FIG. 1 illustrates one representative an embodiment of early stageworkflow in processing data. In general data are collected from ameasurement system step 1002 and pre-processed steps 1004 and 1008. Thispre-processing would depend on the data-collection technology-specificproperties and are assumed to be carried out, unless mentioned otherwise(if needed, prior to applying embodiments of the teachings describedherein). Such pre-processed datasets are denoted as starter datasets andindicated by letter D step 1006 in the rest of the document and in thefigures. Some other figures are referred to in this overview depicted inFIG. 1 (FIG. 2 a- to FIG. 4 step 1010, FIG. 8 step 1012 and FIG. 9 step1014). Aspects of FIG. 2 a through FIG. 4 depict a response surfaceapproach proposed to study the properties of a given data design thatwould (i) aid high-confidence data analysis, and (ii) conversely, aiddevelopment of design principles for a given system using some initialproperties of the experimental and technological aspects. FIG. 14depicts a new normalization scheme that is motivated by biologicalinvariance principles. FIG. 9 depicts application of these two aboveembodiments in combination or using the first aspect alone, togetherwith methods for data specific thresholds for parameters used in theirapplication in a new summarization scheme as well as in high-confidencedifferential identification between datasets representing differentobservations of experimental or natural processes. Variations anddetails of some individual steps are referred to in those figures asadditional figures with appropriate figure numbers. While many of theteachings presented herein relate to large scale datasets with multiplemeasures of each parameter in each observation set many individual stepssuch as normalization scheme, the equations used to optimize selectionof true and false positives in comparative evaluations, methods fordetermining data-specific thresholds and evaluating the statistic ormathematical criteria used for identifying differentials are applicableto many other types of datasets that need not involve multiplemeasurements of each parameter.

FIG. 2 a, 2 b show an embodiments of the method of these teachings. Oneinstance has a tester system with built-in true and false positivesmixed into the system, step 1016, or to mix an appropriately simulatedtrue and false positives step 1020 (for example using techniquesdescribed in developing the methods and algorithms referred to as DaSTand SCALEIT), described below. In one embodiment, the method of thisteaching includes optimizing the identification of differentials betweendatasets maximizing the identification of true positives and minimizingthe identification of false positives. In one instance, a metric termedN_(eff) (for effective number of differentials) is utilized. In oneembodiment, the following equation is utilized (also used in FIG. 2 bstep 1022)—alternative forms suited for specific applications can beused for this purpose (FIG. 2 a, step 1024).

N _(eff)=TP*TP/(TP+FP)*(1−FP/TP)

In one instance, a response surface of Neff with differing values of N(number of independent measures) of that parameter in that datasetincluded and any appropriate statistical/mathematical measure ofconfidence of the determination F (i.e., differential against thenoise)—e.g., Student's t-test for pair-wise comparison of datasets (withreplicates) or Fishers test for comparing multiple groups of data—is asurface with multiple maximum and minimum points on the surface. Anexample, these teachings not be limited to that example, is shown inFIG. 16 with GeneChip® datasets and pair-wise comparisons comparingknown true positives (TPs) of two fold change and a large number ofinvariants (false positives—FPs) between datasets. In FIG. 16, theDataset used is Affymetrix Latin Square Experiments (2 to 7) with threereplicates each using U133A-TAG chip (available athttp://www.affymetrix.com/support/technical/sample_data/datasets.affx).The normalization used in the results shown in FIG. 16 was scalingaverage of all PM and MM intensity values between values 46,000(saturation) and overall chip background (28) to 500. Intensity measureused in the results shown in FIG. 16 was PM−MM, for each probe pair.Parameters in the results shown in FIG. 16 are d′=B′=28; r′=1.1(estimated for use as proof of principle for Response surface strategy).Statistic used in the results shown in FIG. 16 is Student's t-test (tused instead of abbreviation F′ in text). AvgA and AvgB are used insteadof max and min in FIG. 3 a. Ranges used in the results shown in FIG. 16are N (minimum number of informative probe pairs)=3-11, increments of 1and at statistic of 3-10, in increments of 0.5; referred to as F and F′herein.

The response surface of N_(eff) step 1022, in FIG. 16, indicates a broadrange of t statistic and a range of N (independent measures included)that gives near maximal value of N_(eff). In one embodiment, a costfactor involving N and F (symbol F is used as the measure of anystatistic/mathematical measure of confidence used throughout thedocument) is defined. The lower the F and N that gives the substantiallyoptimal combination of true and false positives, the better the abilityto detect small changes with sensitivity. Increased specificity wouldresult from the use of multiple independent measurements in its fullform (i.e., without summarizing to a single value) in the analysisschema. It should also be noted at this stage that typically in analysisof large-scale datasets the problem of false positives is more rampantand less desirable than some loss in true positives (which by nature ofexperimental variability and small number of replicates would even bedesirable in some instances). However, it should be noted that theseteachings are not limited to the above described typical example. Theequation below (also used in FIG. 2 b step 1026) proposes one instanceof a form of cost, the term CANeff for cost adjusted Neff), in terms ofan additive factor of the statistic and the number of independentmeasurements included.

CAN _(eff) =N _(eff)/(F′+N′)

As indicated in FIG. 2 a (step 1028), other effective forms of cost maybe possible and might be desirable in some instances. The calculation ofF′ (the statistical or mathematical confidence threshold) and N′ aredescribed in FIG. 3 and figures referenced therein. Use of a set ofcommon N′ measures for each parameter in all studies relating to adataset or data from the same application (termed Chosenset—step 1122,FIG. 10) is described herein below. Typically, these teachings not beinglimited to the typical example, it has been observed that once theparameters for a technological platform has been calculated using welldesigned true and positives the same set of parameters seem to beapplicable for other datasets from that technology (e.g., FIG. 3, step1030). An alternative strategy that eliminates the need for iteration todetermine F′ as described above but determines a data specificthreshold, is described in FIG. 6 and FIG. 7. In the embodiment shown inFIG. 6 and FIG. 7, substantially optimum parameters for F′ and N′ wouldstill need to be determined based on knowledge based on test cases runusing algorithm in FIGS. 3 a, 3 b starting step 1032 and FIGS. 2 a, 2 bsteps 1026 and 1028.

Reverse application of the above described teaching would be tocollect/simulate preliminary measures using multiple measures for eachparameter (typically more than estimated need) in one or more likelyscenarios of the use of that technology platform or a data collectionstrategy and based on calculated values of d′, r′ and F′, andadditionally using required confidence for that application, the optimalnumber of N (multiple independent measures) would be designed in thetechnology or the data collection strategy. An embodiment of the methodfor the devising of measurements includes obtaining a relationshipbetween one or more preselected parameters and one or more performanceindicators for the measurement of the data set, selecting a metric basedon the at least one performance indicator, applying an optimizationtechnique, and obtaining, from the results of the optimizationtechnique, one or more substantially optimal values of the one or moreparameters. The one or more substantially optimal values of the one ormore parameters enables devising the measurement/collection strategy ofthe data set.

FIG. 3 a and FIG. 3 b depict an algorithm to study these behaviors anditeration over the parameters to determine the substantially optimalthreshold. The method described in FIG. 3 a and FIG. 3 b includesiterating over possible values of N (number of independent measuresincluded, steps 1032 and 1032 b) and over a range of user determinedconfidence threshold of F (when there are more than one replicatedgroup, FIG. 3 b—step 1032 b). The datasets could, in one instance, becomposed of two or more observations, or groups of replicated datasetrepresenting properties of different process states. The increment foriteration over N (N_(inc)) would be 1 (as this represents the number ofmeasures), and for F (F_(inc))—step 1032 and 1032 b, FIG. 3 a and FIG. 3b, respectively—would be determined by the user based on computationaland other resources and the goals of the data analyses. Each parameter(i) is evaluated to satisfy a set of noise threshold criteria andconfidence measures on a comparative basis (i.e. between twoobservations or between sets of replicated observations classified intogroups) as described below. In one instance, only measures thatsatisfies the noise control criteria mentioned below and in FIG. 3 astep 1036 and FIG. 3 b step 1036 and step 1046 are used.

$\left\lbrack {\sum\limits_{j = 1}^{M}\left( {\left. x \middle| {F>=F^{\prime}} \right.,{{x_{jA}/x_{jB}}>=r^{\prime}},{{{x_{jA} - x_{jB}}}>=d^{\prime}}} \right)} \right\rbrack>=N^{\prime}$

(It should be noted that other predetermined criteria are also withinthe scope of this teachings.) where x_(jA) and x_(jB) above refers tosignal of that measure for that parameter being evaluated (x) betweentwo conditions designated A and B, and j running over the M measures ofthat parameter i. F applies to cases with replicated groups in thedataset (step 1046). In FIG. 3 a and FIG. 3 b the terms max and min areused in step 1036 to represent a general case where max refers tomaximum and min the minimum of the two values in case of single valuesbeing compared, maximum/minimum of two averages or medians ormaximum/minimum of the group with the lower average or median. In allthe examples used in the document to demonstrate the utility of theseteachings, average is used when groups are being compared. Optionally,when all the data points of a measure j of that parameter beingevaluated for differential are below a calculated or estimated overallbackground noise (B′—typically determined below which most datacollected represent parameters below reliable detection threshold ofthat measurement system under the conditions used), they are eliminatedfrom analysis step 1048. These thresholds (d′, r′ and B′) avoiddifferentials in the noise range—this aspect is discussed in more detailin a future section. The algorithm for calculating dataset-specificthresholds on distance (d′) and ratio (r′) are described in FIG. 5. Whenthe evaluation of a measure satisfy these criteria it is used in themeasures included in the analysis (step 1050) and the next measure isevaluated. This is repeated for all the measures of a parameter (step1034). When the number of measures passing the above criteria exceedsthe threshold number of measures for that iteration (step 1052), thenthat parameter is considered differential between the observations (orgroups) being compared. When all the parameters are evaluated theresults are for that set of threshold used in that iteration arerecorded (step 1054) and the values of the parameter thresholds areincremented and used for the next iteration (step 1058). Once the rangeof iterations are covered using the increments specified all the storedresults are used to select the substantially optimal combination ofN′—and F′ in case of multiple replicated groups as in FIG. 3 b—(step1056), one embodiment of which is described in FIG. 2, using known orsimulated differentials.

FIG. 3 b, which is an extension of FIG. 3 a deals with the case ofmultiple replicated groups involves optimization of two parameters, thenumber of measures of that parameter (N′) and a confidence measure (F′).The use of the confidence measure based on replicated observations incombination with multiple measures substantially improves thecomparative analyses of the data. In this case the iterations arecarried out similar to that of FIG. 3 a but for each increment of F inthe range selected (i.e., F′ for that iteration), the values asdescribed in FIG. 3 a above are calculated for the whole range of Nthrough iterative loop with changing N′ (steps 1032 b and 1058 b). Thespecifics of the strategy are nearly identical except that for eachmeasure and for each evaluation cycle the confidence measure F (step1044) that is calculated on a comparative basis between two replicatesshould also exceed the threshold F′ (step 1046).

FIG. 4 (optional step 1040, FIG. 3 b) depicts a strategy that eliminatessome groups (in multi-group comparisons) based on these thresholdingstrategies and allows varying group number based differentialidentification for each measure to be evaluated. In this case the noisethresholding is based on comparison of average values over all G groups(termed AvgT step 1060) to that of individual group for each parameteri. As in the previous case average could be replaced by median ormaximum and minimum of the groups or over all groups as described forFIG. 3.

FIG. 17 depicts an example of the behavior of CAN_(eff) with varyingvalues of measurements included (N) and of the statistic (t-statistic inthis case) for the same comparison shown in FIG. 16. It can be seen fromFIG. 16 and Table 1 that (i) the nearly flat surface in FIG. 16 of theresponse surface of N_(eff) can now be reduced to a few distinct peaks,and (ii) the statistical threshold is much lower than that of commonlyused data analysis threshold for p value of 0.05.

TABLE 1 An example of the effect of different statistical threshold (F′)and number of independent measurements used (N′) on the true and falsepositives (of two fold change) identified 3, 6 3, 7 4, 6 4, 7 6, 6 7, 512, 6 7.71, 6  0* 1 0 0 0 0 0 0 0    0.125 4 1 3 1 3 3 1 2   0.25 3 1 31 1 1 1 1   0.5 1 1 1 1 1 1 0 1  1 5 5 5 5 5 6 4 4  2 7 6 6 6 6 6 5 6  48 8 8 8 8 8 6 8  8 8 8 8 7 7 8 7 7 16 8 8 8 8 8 8 8 8 32 9 9 9 9 9 9 9 964 9 9 9 9 9 9 9 9 128  9 9 9 9 9 9 9 9 256  9 8 8 8 8 8 6 8 512* 9 9 99 9 9 9 9 CR^(†) 5 4 5 4 4 5 3 4 Total 95 86 91 85 87 89 77 85identified Total 135 135 135 135 135 135 135 135 present FP 16 2 5 0 0 10 0 PPV 0.86 0.98 0.95 1.00 1.00 0.99 1.00 1.00 Sensitivity 0.70 0.640.67 0.63 0.64 0.66 0.57 0.63

Indicated in Table 1 are the number of spike-ins of two fold differenceidentified at each threshold (out of 9, three in each comparison forthree individual comparisons). The concentration of the spike-in (in pM)are indicated in the leftmost column in each case the concentration ofthe spike-in in the other dataset is twice this amount (except asindicated below). The threshold of t-statistic (F′) and number of validprobe-pairs (N′) is indicated in the first row as (F′,N′). FP is numberof false positives, PPV is positive prediction value [TP/(TP+FP)],sensitivity is [TP/(TP+FN)]. * 0 pM spike-in was compared to 0.125 pMspike-in, and 512 pM spike-in is compared to 0 pM spike-in. † CRindicates cross-reactive transcripts/probesets with homology tospike-ins (out of 9, three in each comparison for three individualcomparisons). The dataset are the same as used in example shown in FIG.16 and FIG. 17. (Note that, in FIG. 17, t used instead of F′ above andthat N′ is equal to the number of probe pairs.)

The example shown in Table 2 demonstrate the significant advantages ofthese findings, i.e., ability to select true positives without muchimpact on the number of false positives identified even at lowerconfidence thresholds. Further this precludes the need for guessing thethreshold. Strategies for estimating data-specific thresholds aredescribed later (FIG. 5, FIG. 6 and FIG. 7). Some aspects ofapplications of this invention in the context of gene expressionmeasurements using GeneChip® technology are described in Gopalan, GenomeBiology 2004 5:p 14, which is incorporated by reference herein.

TABLE 2 Application of data-scaling strategy (SCALEIT) to identifyutility of the Response surface assisted strategy 1.5 2 3 4 3, 5 928713595 18001 19251 3, 6 8548 11031 15101 16657 4, 6 7553 12753 1694718287 4, 7 6927 10333 13965 15431 6, 6 7418 11444 15235 16677 7, 5 858813500 17426 18690 12, 6  5164 8993 12204 13596 7.71, 6   6634 1058414111 15600

Indicated in Table 2 are the number of probesets (average of threeindependent comparisons) detected (out of possible 22,301) at the giventhresholds of t statistic cut-off (F′) and minimum number of probe-pairs(N′) satisfying this F′, indicated as (F′,N′) in column 1. For thepurpose of this evaluation three replicates were compared to three otherindependent replicates essentially representing the same samples scaledto the given differential (indicated in first row), and the valuesindicated are averages of three such independent evaluations. Again, thedataset used are the same as used in example shown in FIG. 16 and FIG.17.

Embodiments of the method of this teachings which utilize (and areutilized in) the above described Response surface assisted thresholdingstrategy (ReSurfX) embodiment for identification of differentials usingdata-specific thresholds are described below.

Some of the embodiments described above utilized a dataset specificallydesigned for such purposes. Many currently existing datasets seldom aredesigned with built-in true and false positives, or not in sufficientnumber and variety. One embodiment, for the instance in which there isnot a sufficient number of variety of true and false-positives utilizesa tester dataset as above to determine thresholds that could be usedwith that type of data generation technology. The use of distance andratio thresholds have already been demonstrated in several conventionalanalyses schemes, but, in this teachings, algorithms for determiningdata-specific thresholds of these parameters are disclosed.

Embodiment for determining data-specific thresholds (DaST) of distance,ratio and statistic to avoid differentials in the noise range aredisclosed herein below.

Different data collection platforms, pre-processing schemes (backgroundcorrection, normalization etc.) and experimental systems have differentlevels of inherent and other handling based noise/variability (typicallyobserved when comparing data between replicates).

FIG. 5 depicts a schema that determines data-specific thresholds fordistance (d) (i.e., numerical difference between the two values or twogroups) and ratio (r) that would typically lie within noise level forthat data. In one embodiment, a percentile is determined at which thesevalues d and r would be optimum based on the ability to detectsubstantially optimal combination of true and positives from a testerdataset, e.g., using N_(eff) step 1022. For this purpose, a large enoughrandom sampling of the data—step 1062 (or the whole data, step 1064) isselected and the distance and ratio are determined between the maximumand minimum for each selected measure for example within replicates(thus capturing the noise component of the data, step 1066). Thecalculated distances and ratios (individually) are sorted in ascendingorder of values (of d and r) and values of d and r at differentpercentiles on the ordered set of values are chosen as thresholds (d′and r′)—step 1072—and used as described in applications described inprevious sections or in determining thresholds for many data analysesscheme (either for selection or for elimination to avoid dealing withdata just in noise range). The different thresholds are tested on atraining set and optimum value chosen (for example by using equation forN_(eff)). This percentile value can be used to determine d′ and r′ (theselected thresholds—DaSTd′ and DaSTr′) step 1074. When additionalspecificity or safeguard is warranted scaled up versions of thedetermined values of d′ and r′, or a percentile threshold above thatdetermined as optimum using the algorithm in FIG. 5 can be used toincrease the confidence level. Dynamic thresholds can also be determinedby using similar strategies on a data ranked by values of the measuresat different points along the distribution and assuming piecewiselinearity (step 1076).

FIG. 6 and FIG. 7 describes similar embodiments, but with additionalintricacies for the determination of data-specific threshold of F (themeasure of confidence used) to avoid differentials primarily within therange of noise (hence few true positives in those ranges). In thisinstance, a large enough sample of parameters and all its replicates areused and additional values within the range of values represented by thereplicates are simulated, step 1080. As warranted, this range can bescaled up by a factor, termed vibrate factor—v (e.g., v=r′, would implyfind enough number of random values between r′ times the maximum valueand (1/r′) times the minimum value)—step 1082. Using just the maximumand minimum value as range would be equivalent to using a vibrate factorof 1.0. The values for that parameter and the random values within(inclusive of the end points) are sorted to form enough groups, step1084, with appropriate number of replicates and the measure ofconfidence calculated, step 1090. In case of multiple independentmeasurements of the parameter, as is the main theme of this section,this process is repeated N′ (threshold number of measurements) times andminimum value is stored as one value of the dataset to be used fordetermining the substantially optimal threshold step 1092. The collectedminimum values are sorted descending and the value of F is chosen at auser determined confidence threshold, DaSTF′ (e.g., 95% confidence levelwould be vale at 95^(th) percentile), step 1094. This value can eitherbe chosen on user determined confidence level or iterated for using atraining set, step 1096. The noise range elimination strategiesdescribed earlier steps 1036 and 1048 (steps 1086 and 1088 in thisalgorithm) could optionally included in calculating DaSTd′, DaSTr′ andDaSTF′. Alternate manifestations of step 1092 could include median orany other percentile of values calculated for the N′ measures of eachparameter, rather than the minimum over the N′ values of F.

When informative N is greater than N′ the statistical threshold can berelaxed (for more sensitive identification of differentials), usingbasic statistical principle of independence (viz., p^(N′)=p₁ ^(N)). Asmentioned before these data types do not exactly satisfy statisticalindependence principle, but the advantage obtained through thisadjustment does not seem to come at recognizable cost in cases tested.

The above embodiment has been applied to a published defined dataset (asan example, embodiments not to be limited to applications or datasets oftype used in this example) with large number of differential andinvariant parameters without iterating over range of N and F values asin example 1, with good success (FIG. 16), by using the strategiesdescribed in FIG. 5, FIG. 6 and FIG. 7 and applying the results to FIG.4. For this purpose N′ value was set as 50% of all probesets(independent measures) available, based on prior trials with data usedin example results shown in Tables 1 and 2 (Table 3).

TABLE 3 Application of data-specific thresholding strategy (FIG. 5-FIG.7), BlNorm scheme (FIG. 14), and ReSurfX (FIG. 3) on a test dataset withlarge number of true and false positives ResurfX identified Choe et.al., Design TPs FPs Chip type DrosGenome1 Total probesets used 3919Total non-differential 2588 Total differential 1331 937 73 >=2 fold 781732 >=1.5 fold 1129 921  <1.5 fold 202 16 Total probesets not used 10091

The dataset used is from Choe et. al., [Genome Biology (2005) 6:R16],which is incorporated by reference herein. The parameters used are

B′=107 (calculated, data not shown)

-   -   i. d′=57 (FIG. 5, at 50th percentile)    -   ii. r′=1.162 (FIG. 5, at 50th percentile)    -   iii. N′=: 7 (estimated—prior art)    -   iv. F′=1.65 (t-statistic—FIG. 6)        Intensity measure used is PM−MM, for each probe pair.        Normalization used is BINorm at 25% middle values in each subset        using known spiked-in invariant set built-in the data. AvgA and        AvgB are used instead of max and min in FIG. 3.

While both these applications are depicted for multiple independentmeasurements it has a broad utility even in datasets with each parameterrepresented by a single value. This can simply be achieved by settingN′=1 in both these cases.

Embodiments of the method of the present teachings for summarizingparameter value includes grouping measurement result from a data setinto a number of pairs of measurement results, determining, for each onepair of measurement results, whether predetermined measures for the onepair of measurement results satisfy threshold criteria, classifying apair of measurement results from the number of pairs of measurementresults as not changing if the predetermined measures do not satisfy thethreshold criteria; comparing, if the predetermined measures satisfiedthe threshold criteria, one measurement result in each one pair ofmeasurement results to another measurement result in each one pair ofmeasurement results, classifying, after the comparison, each one pair ofmeasurement results according to result of the comparison. Forreplicated data sets, the embodiment includes the steps of averaging themeasurement results over replications and grouping the averagedmeasurement results into a number of pairs of averaged measurementresults. The method proceeds similar to the preceding embodiment,utilizing pairs of averaged measurement results instead of pairs ofresults. An embodiment of such method of these teachings, EMIN E: AnExplicit Model INdependent Expression measure, for summarizing parametervalue when represented by multiple independent measures is disclosedbelow.

As described above, conventional summarized values for multipleindependent measures are model based. While such conventionally usedmodel based approaches have significant advantages they may not alwaysbe desirable for all datasets. As described above, use of allindependent measures directly confers significant advantage ofspecificity when identifying differentials between datasets. But suchmethodology has to be adapted for use with other well establishedadvanced statistical and mathematical methods of analysis for patternrecognition etc, especially when the dimensions classifying theobservations and the interactions of interest in the dataset getshigher. And embodiment of a explicit model independent expressionsummary method is disclosed, where the computational and adaptationcosts for using the multiple measures of each parameter does notoutweigh the disadvantages.

FIG. 9 and FIG. 10 describe an embodiment of the method of theseteachings for summary measure using groups of data (typically replicatesof observations in a dataset), while FIG. 8 and FIG. 10 describe asimilar algorithm but for dealing with each observation as single unit(typically unreplicated observations). Each independent measuresatisfying noise threshold criteria i.e., steps 1100, 1102, 1110, 1112and 1114 (as in steps 1036 and 1048) of a parameter is classified as nochange (NC), increase (I) or decrease (D) i.e., steps 1104, 1106, 1108,1116, 1118, 1120 based on pair-wise comparisons, step 1098. Based on asmany comparisons possible (or a minimum number of comparisons when largenumber of combinations are available) the independent measurementssatisfying the specified criteria in the pairs over a particularthreshold of datasets and as many independent measurements havinguniform classification for that parameter are chosen for each parameterstep 1122. When the number of independent measurements chosen for eachparameter is above N′ the values based one reference chip or a set ofchips are ordered and the middle N′ measurements are used forcalculation of expression summaries for all datasets step 1128. Somealternate purpose/technology specific embodiments would include orderingthe usable parameters N based on purpose specific criteria (e.g., alonga predicted transcript and using a set that maximizes chances ofdetecting a variant of the transcript of interest among possiblealternatively spliced forms). When the number of measurements chosen arebelow N′ and the threshold on the number of pair-wise comparison couldnot be relaxed further without deterioration of quality (step 1124) allN measurements satisfying minimum criteria are used (step 1126), sortedand measurements representing middle N′ values chosen. The expressionsummary could be a simple measure such as weighted average with outliercorrection or any other established or modified summary measures step1130. When a number of measurements are available such N′ measurementsthat have uniform property over many comparisons (usually can be set asa threshold percentage of comparisons available to determine thisproperty) a common set for use with that type of dataset for most usesbeyond available or used for this step can be chosen and stored forfuture use. The use of such uniform set of measurements for eachparameter for all datasets, termed the Chosenset step 1122, makes thesummarized values have naturally better quality than using all orvariable number of informative measurements. Use of an additionalappropriate normalization after EMINE may be advantageous in someinstances. One advantage of EMINE is the minimal use of numericalcorrection criteria.

In the context of biological applications, with the development of largescale dataset, a universal set of uniform measurements for EMINE can bedevised and used. The strategy devised above can be interpreted as anapproach to directly achieve this goal.

Embodiment of the method of these teachings for estimating fold changeconfidence estimates of differentials for Response surface based dataanalysis are disclosed herein below.

FIG. 11 and FIG. 12 depict embodiments for determining estimates ofratio of differential (in pair-wise comparisons) and estimate ofconfidence for differentials when using Response surface assistedstrategy, respectively. In the simplest form estimate of ratio isobtained by taking pair-wise ratio for each selected measurement(selection is either based on noise threshold elimination strategies,step 1132) similar to steps 1036 and 1048, using all N passing thresholdelimination, the Chosenset strategy (step 1134), or the N′ valuesnearest to median (step 1136), as described below and in step 1042) ofthat parameter followed by a summary metric—step 1138—(e.g., weightedaverage with outlier correction as in step 1130). When N failing noisethreshold elimination strategy is greater than N′ (step 1140) the failedones can be used for summary measure. When needed middle N′ ratios as instep 1136 can be used. The spread of the estimated ratio for eachparameter over the number of measures used is used to determine andreport an estimate of the ratio. The measure of confidence uses similartechniques (steps 1144 and 1146) except that a minimum value is used togive the most conservative measure of confidence, other variations basedon percentiles of all confidence measures from informative measurementsof that parameter in that comparison could also be used. Wheninformative N is greater than threshold N′, an alternative is to use themiddle N′ values of a sorted (descending) array of F values—step 1148.The confidence measure can then be used as in the cost factor as anadditive measure of N′ and F′ (step 1026) or can be converted to ap-value from a standard statistic or bootstrap based statistics andpresented in desirable format (some usable forms are proposed in FIG.12, step 1150). In the case of using EMINE summarized values, standardmathematical and/or statistical can be applied—steps 1142 and 1152.

An embodiment of a data-scaling method for testing efficacy ofdifferential selection scheme used in analyses of datasets (referred toas SCALEIT) is disclosed herein below.

As has been used extensively in the above sections, a well designedtester dataset would be of extreme value in development and validationof algorithms used in various steps of the workflow. But, such welldesigned tester sets are seldom available that is appropriate for anexperimental scenario, or some times limited by resources. Numerous dataanalysis schemes are used to glean useful information from datasets.Different schemes result in different degree of success (identifyingtrue and false changes and relationships between parameters and/ordifferent observations/conditions being studied). A simulation methodthat utilizes the variances structures present in the whole dataset toevaluate the efficacy of the data analysis scheme applied in a specificexperimental situation is conceived, tested, and described below.

FIG. 13 describes an embodiment of the method of these teachings using adata-scaling approach (SCALEIT), and an example of its utility provided.

Briefly, this embodiment, SCALEIT, involves scaling the whole datasetand its replicates to varying extent (e.g., 1.2, 1.5, 2 timesetc.,)—step 1154—and application of the data analysis/differentialidentification scheme—step 1156. The advantage with this approach beingthe utilization of all possible variance structures inherent to thesystem. An example of this approach in the context of Response surfaceassisted method to identify differentials at various thresholds—step1158—is show in Table 2. Some forms of data analysis schemes would bebetter tested by modifications of this unidirectional scaling strategy,for example bidirectional changes or mixture of such changes suitablycombined with original dataset.

An embodiment of the method of these teachings for normalizing data froma data set includes the steps of sorting data from the data setaccording to measurement value, selecting, according to a predeterminedcriterion, reference subsets, the reference subsets having at least onereference measurement value, selecting, from the sorted data, dataelements having measurement values substantially equivalent to the oneor more reference measurement values, sorting the data elements havingsubstantially equivalent measurement values, the sorted data elementscomprising a sorted substantially equivalent subset, and utilizing theone or more reference measurement values and the sorted substantiallyequivalent subset to normalize the data set. An embodiment of suchteachings motivated by principles of biological invariance to normalizedata, referred to as BINorm, is disclosed herein below.

Array based as well as many other technologies rely highly onnormalization (or some form of numerical equivalency of data) betweendatasets within a platform and across platforms. Most normalization usedto date relies on ordering of datasets and correcting systematicvariations in a intensity dependent manner either using the whole databased distributions, or in spatially separated groups as in print-tipnormalizations (e.g., lowess). Invariably a rank based assumption isbuilt-into the system including nearly exact distribution of datasets,or ordering the whole datasets and choosing rank based invariant setsbetween a reference and a target dataset (e.g. U.S. Pat. No. 6,571,005,which is incorporated by reference herein) or a more recently proposedvariant of the latter method where the dataset is divided into ranges ofexpression values and invariant sets chosen by rank equivalence (U.S.Patent Application Pub. No. 2005/0038839A1, which is incorporated byreference herein). Example of other commonly used methods includeextensive application of principles of variance distributions andattempts to reduce their systematic component using transformations ormodeling). Improper use of normalization scheme can at times introduceartificial bias and error in datasets. An embodiment of the method ofthese teachings, which is motivated by fundamental behavior ofbiological systems, is disclosed below and shown in FIG. 14.

Frequently, in biological systems studying variation of all parametersin one or more experimental conditions there are always a proportion ofrandomly distributed invariant values in any given sample of thedataset. In addition in many systems the variation (or differentials)between experimental conditions and technical variations are random,bidirectional and randomly distributed. Such systems and systems withsmall number of real differences are amenable to this normalizationscheme, termed, BINornn—to indicate biological invariance motivatednormalization. This schema requires designation of one observation asreference—step 1160—and all other observations are normalized withreference to this dataset. Cyclical normalization, i.e., all against allin pair-wise manner might be of use in some instances.

The reference data is ordered by measured values—step 1162—and subsetsare chosen along the total distribution of the data, termed Iref, step1164. The measures equivalent to each subset (i.e., indexes of the datapoints in the subset are used) are chosen from the target data and thissubset sorted, termed Itarget, step 1166. In its simplest form with theabove stated assumption not significantly violated the middle x % ofvalues in the target subset should have equivalent values of the subsetfrom reference array—simplified version of step 1168—(e.g., middle 10%in a 100 point subset of Iref and Itarget). Thus the average (or median)of the x values in Itarget will be equivalent to Iref. The equivalencedetermined this way along the whole dataset would then be used tonormalize using a piecewise linear functionality. The value of x wouldvary with the percentage of invariance and can be iterated upon, step1176, after the above step or on another embodiment depicted in thepicture after iterating on regional equivalence of values in Itarget asdescribed below. As long as the percentage of invariance between thedatasets is above x, there should be no degradation of quality even whenmuch lower percentage, than actual invariance in the data is used.Variations in regional selection of invariance are needed whenunidirectional skew in differentials is present between datasets. Oneembodiment to deal with such cases, represented in steps 1168 and 1170,is to iterate over the equivalent region by scaling the x % of orderedmeasurements of Itarget at different at different percentiles on theordered data (e.g., x % starting at 10^(th) percentile rather then themiddle) and scaling the value to the middle x % of Iref. A built-intraining set, a large enough putative invariant set (see descriptionbelow) can be used to test the quality of the normalization toparticular datasets—step 1172—or using an appropriate test scheme forequivalence. Thus after iterating over the range of percentiles onordered Itarget, the equivalent range chosen to scale the whole datawould be the one that gives the best concordance between the twodatasets as determined with the test using known/simulated invariants oranother test scheme for equivalence—step 1174. BINorm scheme has theadvantage of simple correction of systematic changes while preservingvariability inherent in the experimental design, thus improvingspecificity and confidence in the utilization of resultant inferencesfrom the analyses. An example of such usage with a perfect invariant setis shown in Table 3, though these teachings not being limited to such anexample.

When data from multiple measurement platforms or variations in themeasurement system of the same platform are used, a large enoughpresence of common link terms for the identifiers of the parametersshould suffice to make the measurement values in between the datasetsequivalent and comparable.

As mentioned above, the availability of large scale datasets for eachorganism and platform a large enough putative invariant parameters canbe chosen and used for general purpose analyses of various kinds. Whilenot all parameters may be truly invariant in all conditions being testeda majority should be useful. When most are not utilizable either thenormalization scheme is not applicable to those datasets or that systemis uniquely different.

It should also be noted that though this type of invariance is prevalentin biological systems, any experimental system or datasets having suchproperties are amenable to this normalization schema.

A system and computer program product that integrates the abovedescribed teachings to current databases and other software utilities isdescribed below.

As can be seen in the Figures and the above description, the teachingsand concepts presented hereinabove are presented directly in the form ofalgorithms that are directly amenable to development of computersoftware—step 1182—(in any of the computer languages and user-interfacetools) that can be integrated with databases and data warehouses—step1178 and 1180—as well as ability to use output for other applicationsusing other software or use as input methods/algorithms available inother software packages in conjunction with these teachings—step 1184,1186, 1188 and 1190. A computer usable medium 1179 has computer readablecode embodied therein, where the computer readable code is capable ofcausing the computer system 1175 to execute the methods of theseteachings. Indeed, several of the teachings presented above were testedusing software codes built in the C++ language. (However, the methodsand systems of these teachings are not limited to any one computerlanguage.) In addition these concepts individually can also be used asfunctions integrated inside other packages. A simple schema of anembodiment of a system of these teachings is presented in FIG. 15.

The teachings presented here have the advantage of minimal assumptionsand numerical treatments in most cases thus adding to the goal of highconfidence utilization of large-scale and many high-throughput data—step1192. The concepts and algorithms for applicability for multipleindependent measures of a parameter also would have applications in manyother scenario (e.g., certain kinds of analysis of time course data,collection of meta-data as each parameter). While the utility arediscussed in the context of high-throughput and large-scale organismal(or genome wide) data in biological contexts it should have utility invariety of other contexts where the possibility of application of theconcepts and algorithms exist.

In order to better describe these teachings, the following exemplaryembodiment, these teachings not limited to that embodiment, is presentedbelow. The GeneChip expression data set used in these analyses is fromthe Affymetrix dataset released for purposes of algorithm development,and based on HG-U133A-Tag arrays Experiments 2 through 5, replicates R1through R3. This data set was generated using a hybridization cocktailconsisting of specific RNA spike-ins of known concentration mixed withtotal cRNA from HeLa cell line, by Affymetrix. All probesets startingwith AFFX not part of the spike-ins of known concentration were removedfor calculation of true and false positives involving spike-ins, sincesome of them had obviously discernible differences. Three probesets werereported to have perfect homology of 5 or more probe-pairs thus leaving45 true positives and 22,185 false positives for each comparison in thedataset. Unless mentioned otherwise, values represented are based onaverage of three comparisons between experiments differing in spike-inswith two fold difference in concentration viz., experiments 2 with 3, 3with 4 and 4 with 5. Probe level data were extracted from Cell files(using tiling coordinates defined by probesequence information suppliedfor the chip type—U133A-Tag by Affymetrix) and the mean of all signalvalues (of perfect matches and mismatches that were between the value 28(the lowest background in the chips used) and a saturation value of46,000) were scaled to target value of 500.

b is the background of that chip (as determined by Microarray Suite5.0). When more than 11 probe-pairs represented a probeset only thefirst 11 (in their order of listing in Affymetrix probesequence file)were extracted and used. The difference between perfect match andmismatch value for each probe-pair was used for all further evaluations.Zero or negative differences were set to background.

The signal values were extracted using Microarray Suite 5.0 (Affymetrix,Calif.) with the trimmed mean (top and bottom 2% signal values aretrimmed) for each array scaled to a target intensity of 500, forrepresentation in FIG. 3. Standard definitions for sensitivity andpositive prediction value (PPV) were used. Sensitivity was calculated assn=TP/(TP+FN); PPV was calculated as: PPV=TP/(TP+FP), where TP is truepositives, FP is false positives, and FN is false negatives. Typically,variance weighted average were used, as mentioned.

For the preliminary evaluation on biological replicates, the data fromhuman patients with aortic stenosis (samples JB-as_(—)0806,JB-as_(—)1504 and JB-as_(—)1805 were comparedagainst JB-as_(—)2111,JB-as_(—)2604 and JB-as_(—)2708, hybridized to U75-Av2 chips), fromGenomics of Cardiovascular Development, Adaptation, and Remodeling site,NHLBI Program for Genomic Applications, Harvard Medical School. Thischip consisted of 16 probe-pairs for most transcripts and the averagebackground was used as 60. Calculations were performed using C++ onMS-Developer environment in Windows XP background.

Typical analysis of GeneChip data for identification of differentialsbetween datasets involve extraction of the probe level data using anunified expression index signifying the estimated level of expression ofthat transcript summarizing the information in the eleven or moreprobe-pairs, following normalization or scaling. Some common methodsused for this purpose are dCHIP, RMA and MAS (Microarray Suite,currently version 5.0, Affymetrix, Calif.). The use of unifiedexpression index is advantageous in terms of computational simplicityand easy adaptation of statistical methods to high dimensional datasets.But, due the extremely variable behavior inherent to each proberepresenting the transcript the unified expression index do not alwaysperform satisfactorily. Consequently, statistical approach to reductionof false positives based on ordered statistics or other Bayesianapproaches does not satisfactorily address the issue of false positives.This aspect has recently been evaluated for a few test datasets such asthe one used herein. While improvements in the aforementioned aspectsare constantly being proposed, statistics applied directly toprobe-level data is an attractive alternative. As discussed earlier,several biological and sequence related issues complicate simpleselection of a statistical threshold such as a p-value when using theStudent's t-test. The following approach is motivated by the fact thatthe multiple independent features measured signifying the expressionlevel of a transcript should in principle allow selection of a thresholdthat is appropriate to the noise in a particular data set. In many wellbehaved dataset this threshold should be lower than a commonlyacceptable threshold, e.g., t signifying p<=0.05.

In order to study the performance of differential expression measured atprobe level the response surface of sensitivity, positive predictionvalue, number of true positives and number of false positives wereevaluated as a function of number of valid probe-pairs and a range ofvalues for t (the Student's t statistic). This was done with triplicatedatasets that had spike-ins of two fold difference with differentprobesets in concentration ranges (0-512 pM) between the two datasets. Avalid probe-pair was defined as one that has a minimum difference ofaverage signal value (difference between signal for perfect match andmismatch) above background, and the ratio of averages is at least 1.1(selected intuitively, but can be determined empirically for differentdatasets) and above threshold t, to avoid values in very close range. Inaddition, a condition that there are no more than one-fifth theprobesets that had change in opposite direction was enforced. In generalthis latter condition was never a determining factor in selection ofdifferentials in this dataset. This selection criteria for can beexpressed as:

$\begin{matrix}{\left\lbrack {\sum\limits_{i = 1}^{m}\left( {\left. n \middle| {t>=t^{\prime}} \right.,{{x_{ie}/x_{ib}}>=1.1},{\left( {x_{ie} - x_{ib}} \right)>=b}} \right)} \right\rbrack>={np}} & \lbrack 3\rbrack\end{matrix}$

where n is the number of probe-pairs satisfying the conditions, t′ isthe threshold for t statistic, np is the threshold for number of validprobe-pairs, xie and xib is the signal value for probe-pair i, inexperimental and baseline chips, respectively. The above equationrepresents selection of probesets where the chip designated theexperimental chip has higher value than the chip designated the baselinechip, the equation for probesets with value for baseline chip higher canbe obtained by interchanging xie and xib. For example for a probesetthat satisfies the threshold of 6 valid probe-pairs and t value of 7.0,at least 6 probe-pairs representing that probeset will individually havea t-statistic of 7.0 or above—all having the same direction of change.As can be seen from FIG. 18A, and as expected, with increasing thresholdof t and probe-pair threshold the positive prediction value (PPV)increases i.e., a decreasing number of false positives are identifiedand sensitivity decreases i.e., lesser number of true positives areidentified as differentials. FIG. 18B, shows the decrease of true andfalse positives with increasing threshold of t and up.

The above problem can in principle be viewed as area under the Receiveroperating characteristic (ROC) curve problem with two dimensions tthreshold as one dimension and number of valid probe-pair number asanother dimension. In this kind of situation, one would expect multiplethresholds involving the two dimensions that would have optimal areaunder the ROC curve. Alternatively, this can be viewed as anoptimization problem with the goal of detecting as many true positiveswith optimal combination sensitivity and positive prediction value Inother words this can be written mathematically as, termed effectivenumber of positives identified (Neff):

N _(eff)=TP*TP/(TP+FP)*(1−FP/TP)  [4]

FIG. 16 shows the response surface of this effective number of positivesas a function of t and number of valid probe-pairs (np). It can be seenfrom the figure that a range of t and np can result in comparable Neff,with top two Neff at (t′,np) of (7,5) and (6,6) with (true positives,false positives) of (91,1), (89,1) and (87,0), respectively. The totalpossible number of true positives and false positives were 135, and66,555, respectively. It should be noted that the lowest differential(two fold) was used from the dataset, higher differentials would lead toidentification of higher number of true positives. The presence of alarge portion of the surface across a range of t and np having similarNeff in FIG. 16 suggests that it would be possible to achieve goodsensitivity and selectivity for many np and t values thus potentiallyincreasing the sensitivity of detection of small differentials anddifferentials in transcripts expressed at low levels. This can beachieved in principle by defining a cost factor consisting of the twoparameters being tested. One form of defining such a cost adjustedeffective number of positives picked (CANeff) would be:

CAN _(eff) =N _(eff)/(t′+np)  [5]

The response surface for CANeff as a function of t′ and np is shown inFIG. 17. It can be seen from the surface of CANeff (FIG. 17) that thelargely flat area near the peak of Neff (in FIG. 16) can now be reducedto a few distinct and narrow peaks. The (t′,np) values yielding the topthree CANeff are (3,7), (4,6) and (4,7) with (true positives, falsepositives) (86,2), (91,5) and (85,0), respectively. It should behighlighted that these values of true and false positives selected atthis threshold are comparable to that of the maximum Neff mentionedbefore. For comparison, at t signifying p<=0.05 and a threshold of sixvalid probesets the (true positives,false positives) was (85,0). Thenumber of true and false positives identified and the concentrationrange of the spike-in positives for a selected set of t′ and np valuesare summarized in Table 1. The possibility of selecting a lowerthreshold and still being able to maintain high selectivity wouldespecially be of interest (i) with certain datasets where there is alarge increase in positives with a small reduction in threshold, whereasthe training dataset indicative of variability in the experiment suggestthat this would result in a very small number increase in selection offalse positives, and (ii) for sensitive identification of smalldifferentials without significant loss of selectivity (illustrated inthe next section with some test cases).

The methodology outlined above is termed ResurfP, for Response surfaceassisted Parametic test. It should be noted that lower the thresholdthat can give good selectivity, the better it is to select smalldifferentials and differentials in transcripts with low expressionlevels. Thus, the advantage of the lowered threshold were evaluated byscaling one of the two datasets (i.e., the probe level data extracted asoutlined herein) used in above comparison to varying extents (1.5, 2, 3and 4 fold) and comparing to the other dataset. This should allowcomparison of data classes with wider variety of variances as opposed toa few signified by the spike-ins. Further, this should also reveal thesensitivity of the methodology in the context of technical replicates,thus revealing the maximum achievable sensitivity. The results for thisevaluation at the thresholds yielding the top two CANeff, t signifyingp<=0.05, and the threshold specifying the top Neff are represented inTable 2. As expected, the lower thresholds lead to higher sensitivity ofdetection at any given level. It should be noted that even at the lowerthreshold (t′, np) of (3,6), the differentials (average of threecomparisons compared to maximum identifiable differentials definedbelow) identified were only 42%, 61%, 81% and 86% of 1.5, 2, 3 and 4fold respectively, which further emphasizes the need for and importanceof the proposed approach. At a threshold of (7.71, 6) these values weresignificantly lower viz., 30%, 47%, 63% and 70%, respectively. For thepurpose of calculating percentage of differentials identified themaximum identifiable differentials was set at 21,485, which is thedifferentials (average of three comparisons) identified at the thresholdof (t′=4, np=5) with a scaling factor of 10. A steep decline face on thesurface of FIG. 17 (right hand side) with increasing probe-pairthreshold together with results indicated in Table 2 also indicate ahigher penalty for increasing the probe-pair threshold than forincreasing t statistic threshold. Additionally, these data indicate thatan appropriate choice of a lower probe-pair threshold can lead tosignificantly higher number of true differentials without concomitantincrease in false positives. In order to have a preliminarycharacterization of the nature of probesets/transcripts that areselected and are missed in this study, the distribution of theexpression indices (to simplify the representation) of these probesetsfor one of the thresholds (t′,np) of (3,7) is shown in FIG. 19. As canbe seen from FIG. 19 and as expected the distribution of the expressionindices of probesets, low expressors are detected better at higherdifferential ratios. Conversely, almost all the probesets missed athigher differential ratios were low expressors, which is consistent withobservations that there is high variability in the low detection ranges.

The optimal application of ResurfP on biological samples with differentproperties need additional testing with an independent confirmationusing another technology. Nevertheless, the results of a preliminaryevaluation to test if the lower threshold identified by ResurfP wouldlead high false positives when tested on biological replicates are veryencouraging. For this purpose (t′,np) thresholds of (3,6) and (3,8) weretested on one set of biological replicates from cardiogenomics website(see methods). For this purpose, data from six human patients withaortic stenosis were split into two groups (of triplicates) and themethod was evaluated. This lead to identification of only 52 and 21 of12,624 probesets at (3,6) and (3,8), respectively, even though this chiptype consisted of 16 probe-pairs for most probesets/transcripts.

It should be noted that the above exemplary embodiment is presented tobetter illustrate some of the embodiments of these teachings and doesnot limit these teachings nor does the above exemplary embodimentillustrate all of the above described embodiments.

The techniques described above may be implemented in one or morecomputer programs executing on a programmable computer including aprocessor, a storage medium readable by the processor (including, forexample, volatile and non-volatile memory and/or storage elements), and,in some embodiments, also including at least one input device, and/or atleast one output device. Program code may be applied to data enteredusing the input device (or user interface) to perform the functionsdescribed and to generate output information. The output information maybe applied to one or more output devices.

Elements and components described herein may be further divided intoadditional components or joined together to form fewer components forperforming the same functions.

Each computer program may be implemented in any programming language,such as assembly language, machine language, a high-level proceduralprogramming language, an object-oriented programming language, or acombination thereof. The programming language may be a compiled orinterpreted programming language.

Each computer program may be implemented in a computer program producttangibly embodied in a computer-readable storage device for execution bya computer processor. Method steps of the invention may be performed bya computer processor executing a program tangibly embodied on acomputer-readable medium to perform functions of the invention byoperating on input and generating output. Other methods and/or computercodes can provide input to these programs based on combinations ofcomponents herein or take output from these combinations as input.Combinations of input and output, i.e., communicative and integrativeuse of components described herein and other methods or computer codescould also be implemented.

Common forms of computer-readable (computer usable) media include, forexample, a floppy disk, a flexible disk, hard disk, magnetic tape, orany other magnetic medium, a CDROM, any other optical medium, punchedcards, paper tape, any other physical medium with patterns of holes orother patterns, a RAM, a PROM, and EPROM, a FLASH-EPROM, any othermemory chip or cartridge, a carrier wave, such as electromagneticradiation or electrical signals, or any other medium from which acomputer can read.

Although the invention has been described with respect to variousembodiments, it should be realized this invention is also capable of awide variety of further and other embodiments within the spirit andscope of the appended claims.

What is claimed is:
 1. A computer implemented method for devisingmeasurements of fluorescence, wherein a signal is measured at differentpoint along the spectrum of a fluorescent signal being measured, themethod comprising the steps of: selecting a metric for determiningsubstantially optimal combination of true positives and false positivesin at least one data set; applying an optimization technique; andobtaining, from the results of the optimization technique, a value forat least one optimization parameter, said value for at least oneoptimization parameter resulting in substantially optimal combination oftrue positives and false positives; wherein the obtaining at least oneoptimization parameter comprises obtaining a value of a number ofindependent measures; wherein obtaining a value of a number ofindependent measures comprises obtaining at least one combination of avalue of a number of independent measures and a value for a confidencemeasure; said independent measures comprising measures of a parameter offluorescence obtained using different measurement criteria; wherein anumber of true positives and false positives are a function of at leastone combination of the number of independent measures and the confidencemeasure; and wherein—the steps of selecting a metric, applying anoptimization technique, and obtaining, from the results of theoptimization technique, a value are performed by means of anon-transitory computer usable medium having computer readable code thatcauses a processor to perform the steps; whereby such measurement areused in systems used in applications including nucleic acid sequencing,high spatial density measurement of fluorescent based signals usingscanners and cameras including for nucleic acid and proteinmeasurements.
 2. The method of claim 1 wherein the step of applying anoptimization technique comprises the step of optimizing a cost function;said cost function being a function of the number of independentmeasures of fluorescence.
 3. The method of claim 1 further comprisingthe steps of: a) selecting a predetermined initial value of thethreshold for the value of the number of independent measures; b)selecting one element of the data set; the data set comprising aplurality of elements; c) determining at least one predeterminedquantity for the selected one element; d) determining whether said atleast one predetermined quantity substantially satisfies a thresholdcriterion; e) incrementing, if said at least one predetermined quantitysatisfies the threshold criterion, a number of elements; f) determining,after incrementing the number of elements, if the number of elements ismore than the threshold for the value of the number of independentmeasures; g) repeating steps b) through f) for each element from theplurality of elements; h) determining, using step c), whether thethreshold for the value of the number of independent measures results ina substantially optimal combination of true positives and falsepositives.
 4. The method of claim 3 wherein the data set includes atleast two parameters for at least one element; and the method furthercomprises the step of repeating steps d) and e) for each parameterbefore completing step f).
 5. The method of claim 4 wherein the data setincludes replicates; and the method further comprises the step of: i)selecting, before step b), a predetermined initial value of theconfidence threshold measure; j) calculating, after step d), if said atleast one predetermined quantity satisfies the threshold criterion, aconfidence measure for said one element; k) determining whether thecalculated confidence measure is greater than the confidence thresholdmeasure; l) proceeding to step e), for each element from the pluralityof elements; m) incrementing, after step h), the confidence thresholdmeasure within a range of predetermined confidence thresholds; andwherein step d) further comprises repeating steps j) through l); andwherein step h) further comprises selecting the confidence thresholdmeasure that results in a substantially optimal combination of truepositives and false positives.
 6. The method of claim 3 wherein the dataset includes at least two parameters for at least some elements; and themethod further comprises the step of repeating steps d) and e) for eachparameter before completing step f).
 7. The method of claim 4 whereinthresholds for predetermined quantities are determined by the steps of:evaluating the predetermined quantities over at least a portion of thedata set; sorting the evaluated predetermined quantities in ascendingorder of value; and selecting a predetermined percentile of thepredetermined quantity as the threshold for the predetermined quantity.8. The method of claim 7 wherein the predetermined quantity is anumerical difference between two elements of the data set.
 9. The methodof claim 7 wherein the predetermined quantity is the ratio between twoelements of the data set.
 10. The method of claim 7 wherein the step ofevaluating the predetermined quantities over at least a portion of thedata set comprises the steps of: selecting portion of the data set; andevaluating the predetermined quantities over the selected portion of thedata set; and wherein the selected threshold for the predeterminedquantity is utilized for the portion of the data set being evaluated.11. The method of claim 10 wherein the predetermined quantities areobtained by interpolation and extrapolation based on consecutiveportions of the data set.
 12. A system for devising measurements offluorescence, wherein the signal is measured at different point alongthe spectrum of the fluorescent signal being measured, the systemcomprising: at least one processor; and computer usable media havingcomputer readable code embodied therein, the computer readable codecausing said at least one processor to: select a metric for determiningsubstantially optimal combination of true positives and false positivesin at least one data set; apply an optimization technique; and obtain,from the results of the optimization technique, a value for at least oneoptimization parameter, said value for at least one optimizationparameter resulting in substantially optimal combination of truepositives and false positives; wherein the obtaining at least oneoptimization parameter comprises obtaining a value of a number ofindependent measures; wherein obtaining a value of a number ofindependent measurements comprises obtaining at least one combination ofa value of a number of independent measures and a value for a confidencemeasure; said independent measures comprising measures of a parameter offluorescence obtained using different measurement criteria; wherein anumber of true positives and false positives are a function of at leastone combination of the number of independent measures and the confidencemeasure; whereby such measurement are used in systems used inapplications including nucleic acid sequencing, high spatial densitymeasurement of fluorescent based signals using scanners and camerasincluding for nucleic acid and protein measurements.
 13. The system ofclaim 12 wherein the computer readable code in causing said at least oneprocessor to apply an optimization technique further causes said atleast one processor to optimize a cost function; said cost functionbeing a function of the number of independent measures of thefluorescence.
 14. The system of claim 12 wherein the computer readablecode also causes said at least one processor to: a) select apredetermined initial value of the threshold for the value of the numberof independent measures; b) select one element of the data set; the dataset comprising a plurality of elements; c) determine at least onepredetermined quantity for the selected one element; d) determiningwhether said at least one predetermined quantity substantially satisfiesa threshold criterion; e) increment if said at least one predeterminedquantity satisfies the threshold criterion, a number of elements; f)determine, after incrementing the number of elements, if the number ofelements is more than the threshold for the value of the number ofindependent measures; g) repeat steps b) through f) for each elementfrom the plurality of elements; h) determine using step c), whether thethreshold for the value of the number of independent measures results ina substantially optimal combination of true positives and falsepositives.
 15. The system of claim 14 wherein the data set includes atleast two parameters for at least some elements; and wherein thecomputer readable code also causes said at least one processor to:repeat steps d) and e) for each parameter before completing step f). 16.A computer program product comprising a non-transitory computer usablemedium having computer readable code embodied therein; said computerreadable code causing a computer system to: select a metric fordetermining substantially optimal combination of true positives andfalse positives in at least one data set; apply an optimizationtechnique; and obtain, from the results of the optimization technique, avalue for at least one optimization parameter, said value for at leastone optimization parameter resulting in substantially optimalcombination of true positives and false positives; wherein the obtainingat least one optimization parameter comprises obtaining a value of anumber of independent measures; wherein obtaining a value of a number ofindependent measurements comprises obtaining at least one combination ofa value of a number of independent measures and a value for a confidencemeasure; said independent measures comprising measures of fluorescenceobtained using different measurement criteria; wherein a number of truepositives and false positives are a function of at least one combinationof the number of independent measures and the confidence measure. 17.The computer program product of claim 14 wherein the computer readablecode in causing the computer system to apply an optimization techniquefurther causes said at least one processor to optimize a cost function;said cost function being a function of the number of independentmeasures of fluorescence.